# Finding Max Distance between coordinates

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Prabs on 20 Oct 2013
Answered: Alaa on 4 Mar 2015
Hi guys, Urgently need some help on this. I have made a code that analyses any given image and outputs the coordinates of the boundary points into 2 separate arrays, x and y. I want to find the distance between all the coordinates with each other. And then identify the coordinates that give the longest distance.
Thanks

sixwwwwww on 20 Oct 2013
Can you please share your code and image to sort out the solution?
Prabs on 20 Oct 2013
if true
% s=imread('twolines.tif'); %calls the image into matlab
numwhite2 = regionprops(s,'BoundingBox', 'Extrema'); %finds the number of white pixels in the image, although it doesn't show when the image is called.
figure;imshow(s,[]); %graphically shows the image
% -- plot bounding box
figure;
imshow(s,[]);
hold;
h1=rectangle('position', numwhite2.BoundingBox);
set(h1, 'linewidth', 2, 'edgecolor', 'r');
% -- Draw bound on the image
[ilabel, num]=bwlabel(s); [B, L]=bwboundaries(ilabel, 'noholes');
coord=cell2mat(B); x=coord(:,1); y=coord(:,2); plot(y,x,'.g'); coorddata = [x y]; end

sixwwwwww on 20 Oct 2013
Dear Prabs, here is an example code which you can use for this purpose:
x = 1:10; % x component of coordinate
y = 2:2:20; % y component of coordinate
count = 1;
for i = 1:length(x) - 1
for j = i + 1:length(x)
distance(count) = sqrt((x(i) - x(j))^2 + (y(i) - y(j))^2);
Matrix(count, :) = [x(i) y(i) x(j) y(j) distance(count)];
count = count + 1;
end
end
SortedMatrix = sortrows(Matrix, 5);
MaxDis = SortedMatrix(size(Matrix, 1), :);
fprintf('Coordinates of maximum distnace are (x1, y1) = (%d, %d) and (x2, y2) = (%d, %d)\n', MaxDis(1), MaxDis(2), MaxDis(3), MaxDis(4))
fprintf('Maximum distance = %d\n', MaxDis(5))
I hope it helps.

#### 1 Comment

Image Analyst on 20 Oct 2013
You can use a vectorized approach, like I did in the engine at the middle of my code below to have a more "MATLAB-ish" faster, more efficient approach.

Image Analyst on 20 Oct 2013
Edited: Image Analyst on 20 Oct 2013
You can find the distances from a point to all the other points in one single line, assuming you have the x and y coordinates. (Don't be afraid - the main code is only 4 lines long and is at the center between the ----- lines. The rest of it is just to make it fancy by displaying and printing the points.)
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
clc; % Clear the command window.
workspace; % Make sure the workspace panel is showing.
% Initialization code
numberOfCoords = 20;
% Plot the points so we can see them.
x = rand(1, numberOfCoords);
y = rand(1, numberOfCoords);
plot(x, y, 'b*');
hold on;
for k = 1 : numberOfCoords
% Label the kth point in the plot.
text(x(k)+0.01, y(k), num2str(k));
end
maxDistance = zeros(1, numberOfCoords);
indexOfMax = zeros(1, numberOfCoords, 'int32');
%-----------------------------------------------
% Main engine:
% Find the furthest away points.
for k = 1 : numberOfCoords
distances = sqrt((x-x(k)).^2 + (y-y(k)).^2);
[maxDistance(k), indexOfMax(k)] = max(distances);
end
%-----------------------------------------------
% Done! Now show out results in the command window.
% Display in command window.
for k = 1 : numberOfCoords
thisDistance = maxDistance(k);
thisIndex = indexOfMax(k);
fprintf('Point #%d at (%.1f, %.1f) is farthest away from point #%d at (%.1f, %.1f) and is at a distance of %f\n',...
thisIndex, x(thisIndex), y(thisIndex),...
k, x(k), y(k), thisDistance);
end

Alaa on 4 Mar 2015
Please, I have the same problem here:
And your help will be highly appreciated...